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Help with differentiation

y=(x^-3)/2
So far, I have converted it to 1/2x^3. After that, I differentiated it to get 3/2x^2 but this is wrong.
(edited 9 years ago)
Reply 1
Avatar for weasdown
weasdown
2
Bring the power down to the front and reduce the power by one.

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The way you've done it is correct for (x^3)/2 but you haven't taken into account that the 3 is negative in this case.
Reply 3
Avatar for Year11guy
Year11guy
OP
18
Original post by HandmadeTurnip
The way you've done it is correct for (x^3)/2 but you haven't taken into account that the 3 is negative in this case.


I have which is why I converted it to 1/(2x^3). Was I wrong in doing this.
Original post by Year11guy
I have which is why I converted it to 1/(2x^3). Was I wrong in doing this.


Oh, I see. I thought you meant 1/2(x^3).

You don't need to do that, you can just leave it in its original form and go straight into differentiating it. The method is the same as for a positive power, it just requires a little extra thought. For example, x^2 becomes 2x but x^(-2) becomes -2x^(-3).
Reply 5
Avatar for Year11guy
Year11guy
OP
18
Original post by HandmadeTurnip
Oh, I see. I thought you meant 1/2(x^3).

You don't need to do that, you can just leave it in its original form and go straight into differentiating it. The method is the same as for a positive power, it just requires a little extra thought. For example, x^2 becomes 2x but x^(-2) becomes -2x^(-3).


How would I go about differentiating the original equation?
Reply 6
Avatar for Zen-Ali
Zen-Ali
8
Original post by Year11guy
...


Leave the negative index, so that the expression in xx remains at the top, factor out the constant and differentiate using nxn−1nx^{n - 1}.
Original post by Year11guy
How would I go about differentiating the original equation?


Just apply the same method you usually use for differentiation (i.e. multiply the entire term by the power and then subtract 1 from the power).
Original post by frozo123
it's -3/2x^-4


Please don't give full solutions, I was trying to get him to work it out for himself.
Original post by HandmadeTurnip
Please don't give full solutions, I was trying to get him to work it out for himself.

You're the one who has quoted the answer..
Original post by frozo123
You're the one who has quoted the answer..


Nice logic.
Reply 11
Avatar for Year11guy
Year11guy
OP
18
So is the answer: (-3x^-4/2) or what frozo said
Original post by Year11guy
So is the answer: (-3x^-4/2) or what frozo said


−3x−42\frac{-3x^{-4}}{2}, yes.

Do you understand why that's the answer?
Reply 13
Avatar for Year11guy
Year11guy
OP
18
Original post by HandmadeTurnip
−3x−42\frac{-3x^{-4}}{2}, yes.

Do you understand why that's the answer?


Yes. but that seems too easy. I mean what about the 2 on the bottom? Why does that stay? Wouldn't the two disappear after differentiation or do I treat it as a part of the whole term? So for example: is (1x^2)/2 and 1/(2x^2) the same thing?
Original post by Year11guy
Yes. but that seems too easy. I mean what about the 2 on the bottom? Why does that stay? Wouldn't the two disappear after differentiation or do I treat it as a part of the whole term? So for example: is (1x^2)/2 and 1/(2x^2) the same thing?


The 2 is just a constant so that's why it stays. It's probably easier to think of it as 12x−3\frac{1}{2}x^{-3}. You just treat the half the same way as you would any other coefficient.

And no, those two expressions aren't the same thing.

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